Bipolar Pulse-Induced Coexisting Firing Patterns in Two-Dimensional Hindmarsh-Rose Neuron Model

In this paper, a bipolar pulse (BP) current is taken to mimic a periodic stimulus effect on the membrane potential in the axon of a neuron. By introducing the BP current to substitute the externally applied constant current, a BP-forced two-dimensional Hindmarsh-Rose (HR) neuron model is proposed. Based on the proposed neuron model, the BP-switched equilibrium point and its stability evolution with the periodic variation in time are explored. Furthermore, coexisting asymmetric attractors (or coexisting firing patterns) with bistability are revealed by phase plane orbits, time sequences, and attraction basins, as well as the BP-induced coexisting asymmetric attractors' behaviors are then elaborated through bifurcation analysis. The research results exhibit that, with the increase of the time, the stabilities of the neuron model are continually switched between an unstable node-focus and a stable point, resulting in the coexisting behaviors of numerous asymmetric attractors under the specified initials. Consequently, the newly introduced BP current stimulus, instead of the original constant current stimulus, allows the two-dimensional HR neuron model to possess complex dynamical behaviors for the membrane potential. Additionally, a hardware breadboard is fabricated and circuit experiments are carried out to validate the numerical simulations.